One-shot distillation with constant overhead using catalysts

TL;DR

This paper introduces a novel catalysis technique that enables quantum resource distillation with constant overhead in one-shot settings, significantly improving efficiency and versatility in quantum information processing.

Contribution

It demonstrates how quantum catalysts can achieve constant-overhead one-shot distillation, overcoming previous logarithmic bounds and extending to dynamical resources.

Findings

Constant-overhead magic state distillation achieved.

Tunable trade-off between overhead and success probability.

Catalysis extends to dynamical quantum resources.

Abstract

Quantum resource distillation is a fundamental task in quantum information science and technology. Minimizing the overhead of distillation is crucial for the realization of quantum computation and other technologies. Here we explicitly demonstrate how, for general quantum resources, suitably designed quantum catalysts (i.e., auxiliary systems that remain unchanged before and after the process) enable distillation with constant overhead in the practical one-shot setting, thereby overcoming the established logarithmic lower bound for one-shot distillation overhead. In particular, for magic state distillation, our catalysis method paves a path for tackling the diverging batch size problem associated with code-based low-overhead protocols by enabling arbitrary reduction of the protocol size for any desired accuracy. Notably, this first yields constant-overhead magic state distillation methods with controllable protocol size. Furthermore, we demonstrate a tunable spacetime trade-off between overhead and success probability enabled by catalysts which offers significant versatility for practical implementation. Finally, we extend catalysis techniques to dynamical quantum resources and show that channel mutual information determines one-shot catalytic channel transformation, thereby advancing our understanding for both dynamical catalysis and information theory.